Adaptive refinement with locally linearly independent LR B-splines: Theory and applications

Patrizi, Francesco; Manni, Carla; Pelosi, Francesca; Speleers, Hendrik

doi:10.1016/j.cma.2020.113230

Cited by 25 publications

(11 citation statements)

References 26 publications

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“…A refinement algorithm that alternates the refinement direction, similar to the one we detailed for T-splines, has been introduced in [39]. Recently, [169] introduced another refinement algorithm which preserves (local) linear independence of LR-splines. A comparison of LRsplines and THB-splines can be found in [125].…”

Section: Other Splines For Adaptive Methodsmentioning

confidence: 99%

Mathematical Foundations of Isogeometric Analysis

et al. 2020

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isogeometric analysis, with special focus on the mathematical theory. This includes an overview of available spline technologies for the local resolution of possible singularities as well as the state-of-the-art formulation of convergence and quasi-optimality of adaptive algorithms for both the finite element method (FEM) and the boundary element method (BEM) in the frame of isogeometric analysis (IGA).

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Section: Other Splines For Adaptive Methodsmentioning

confidence: 99%

Mathematical Foundations of Isogeometric Analysis

et al. 2020

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“…We compare and summarize the convergence plots of the two geometric On the other hand, it is worth mentioning that adaptive mesh refinement is usually the method of choice to recover optimal convergence for problems with irregular solutions. In IGA, T-splines [51][52][53][54], hierarchical B-splines [55][56][57][58][59], and locally-refinable B-splines [60,61] are typical examples in this family of methods.…”

Section: L-shaped Domainmentioning

confidence: 99%

Immersed boundary-conformal isogeometric method for linear elliptic problems

et al. 2021

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We present a novel isogeometric method, namely the Immersed Boundary-Conformal Method (IBCM), that features a layer of discretization conformal to the boundary while employing a simple background mesh for the remaining domain. In this manner, we leverage the geometric flexibility of the immersed boundary method with the advantages of a conformal discretization, such as intuitive control of mesh resolution around the boundary, higher accuracy per degree of freedom, automatic satisfaction of interface kinematic conditions, and the ability to strongly impose Dirichlet boundary conditions. In the proposed method, starting with a boundary representation of a geometric model, we extrude it to obtain a corresponding conformal layer. Next, a given background B-spline mesh is cut with the conformal layer, leading to two disconnected regions: an exterior region and an interior region. Depending on the problem of interest, one of the two regions is selected to be coupled with the conformal layer through Nitsche’s method. Such a construction involves Boolean operations such as difference and union, which therefore require proper stabilization to deal with arbitrarily cut elements. In this regard, we follow our precedent work called the minimal stabilization method (Antolin et al in SIAM J Sci Comput 43(1):A330–A354, 2021). In the end, we solve several 2D benchmark problems to demonstrate improved accuracy and expected convergence with IBCM. Two applications that involve complex geometries are also studied to show the potential of IBCM, including a spanner model and a fiber-reinforced composite model. Moreover, we demonstrate the effectiveness of IBCM in an application that exhibits boundary-layer phenomena.

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“…al. [17] propose a practical refinement strategy where local linear independence is ensured. A modified structured mesh refinement where some of the splits are prolonged so the refined mesh satisfies the so called non-nested support property is proposed, see [17] for a definition.…”

Section: Refinement Strategies and Success Criteriamentioning

confidence: 99%

Scattered data approximation by LR B-spline surfaces. A study on refinement strategies for efficient approximation

Skytt¹,

Dokken²

2020

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Locally refined spline surfaces (LRB) is a representation well suited for scattered data approximation. When a data set has local details in some areas and is largely smooth in other, LR B-splines allow the spatial distribution of degrees of freedom to follow the variations of the data set. An LRB surface approximating a data set is refined in areas where the accuracy does not meet a required tolerance. In this paper we address, in a systematic study, different LRB refinement strategies and polynomial degrees for surface approximation. We study their influence on data volume and accuracy when applied to geospatial data sets with different structural behaviour. The performance of the refinement strategies is to some degree coherent and the article concludes with some recommendations. An overall evaluation indicates that bi-quadratic LRB are preferable for the uses cases tested, and that the strategies we denote as "full span" have the overall best performance.

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Adaptive refinement with locally linearly independent LR B-splines: Theory and applications

Cited by 25 publications

References 26 publications

Mathematical Foundations of Isogeometric Analysis

Mathematical Foundations of Isogeometric Analysis

Immersed boundary-conformal isogeometric method for linear elliptic problems

Scattered data approximation by LR B-spline surfaces. A study on refinement strategies for efficient approximation

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